We construct families of principally polarized abelian varieties whose theta divisor is irreducible and contains an abelian subvariety. These families are used to construct examples when the Gauss map of the theta divisor is only generically finite and not finite. That is, the Gauss map in these cases has at least one positive-dimensional fiber. We also obtain lower-bounds on the dimension of Andreotti-Mayer loci.

中文翻译：

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其高斯图具有正维数纤维的 Theta 除数

我们构建了主要极化阿贝尔变体的家族，其 theta 除数是不可约的并且包含一个阿贝尔子变体。当 theta 除数的高斯图只是一般有限而不是有限时，这些族用于构造示例。也就是说，这些情况下的高斯图至少有一个正维纤维。我们还获得了 Andreotti-Mayer 轨迹维度的下限。